Taxpayers are spending $3,000 a week to rent a house in Canberra that Prime Minister Tony Abbott does not want to live in.

Mr Abbott has been staying at the Australian Federal Police training headquarters while The Lodge undergoes major repairs.

It has emerged the Department of Prime Minister and Cabinet signed a 12-month lease on a house in August, during the caretaker period.

But department official Elizabeth Kelly says Mr Abbott made it clear shortly after the election he did not want to live there.

She says the department is now trying to terminate the lease.

"Since that time we have been in negotiations with the owner and the landlord and the property agent for the property trying to make arrangements to find an alternative tenant so we could terminate the lease," she said.

"We are still in those negotiations."

Liberal senator Cory Bernardi has questioned why a lease was signed before the election.

"Perhaps well intentioned, but very presumptuous, and I'm not sure the taxpayers will enjoy the fact they've got $156,000 worth of lease payments to pay for an empty building," he said.

The department says it wanted to find accommodation comparable to The Lodge.